What is the mass of a crate if a force of 200 N causes it to accelerate at [tex]$8 m / s ^2$[/tex]? (Formula: [tex]$F= ma$[/tex])
Answer (1)
We are given the force F = 200 N and acceleration a = 8 m / s 2 .
We use the formula F = ma to relate force, mass, and acceleration.
We rearrange the formula to solve for mass: m = a F .
We substitute the given values to find the mass: m = 8 200 = 25 k g .
Explanation
Understanding the Problem We are given the force applied to a crate and its resulting acceleration, and we are asked to find the mass of the crate. We know the formula that relates force, mass, and acceleration is F = ma , where F is the force, m is the mass, and a is the acceleration.
Rearranging the Formula We need to rearrange the formula F = ma to solve for the mass m . Dividing both sides of the equation by a , we get: m = a F
Substituting the Values Now, we substitute the given values into the formula. The force F is 200 N, and the acceleration a is 8 m / s 2 . Therefore, m = 8 m / s 2 200 N
Calculating the Mass Performing the division, we find the mass: m = 25 k g
Final Answer Therefore, the mass of the crate is 25 kg.
Examples
Understanding the relationship between force, mass, and acceleration is crucial in many real-world scenarios. For instance, consider designing a car. If you know the force the engine can produce and you want the car to accelerate at a certain rate, you can use F = ma to calculate the maximum mass the car can have. Similarly, in sports, knowing how much force a baseball bat applies to a ball and measuring the ball's acceleration allows you to determine the ball's mass. These principles are fundamental in engineering, physics, and even everyday activities involving motion and force.
